If the piece looked like a little bouy, then that is the factory plug that goes into the dipstick tube apeture to keep crap from falling in. Toss it. You said you pulled the pan. Is the fluid level fine and the fluid look ok?
If the fluid is low, it will ...lose gear and neutral.... at lights and such and when you rev it and the pump turns, it will suddenly jump into gear and the car will move.
If it's revving past it's normal point and doesnt shift either
1. If it feels like it's neutralling above the normal rpm shift point, you have a stuck valve in the valvebody. Remove valvebody and move everything around till you find the culprit, remove valve and turn in steel wool, reinstert and repeat until it's moving freely
2. If you're powering above the shiftpoint, the TV cable needs to be lengthened since the trans thinks you are at full throttle.
Get under the car at drivers side, about halfway down and feel up where the shifter cable goes in. There will be a second lever there. Make sure it's free moving. There is some way to adjust the clip on the throttle lever below the TB by pushing the clip out but this method never works properly. You want the cable just tuaght when the throttle is closed and fully pulled with the throttle wide open. The factory system is calibrated for factory geometry so I agree the motor mounts are the cause (unless the lever is stuck). Lowering the motor also lowers the trans, remember that.
Here is the standard adjustment method:
http://www.txchange.com/aodadj.htm
Good luck!
CrazyPete